Question 694383
Look at Row 6 in Pascals triangle to see these numbers: 1, 5, 10, 10, 5, 1 



These coefficients multiply with the following terms:


(3v)^5*(s)^0
(3v)^4*(s)^1
(3v)^3*(s)^2
(3v)^2*(s)^3
(3v)^1*(s)^4
(3v)^0*(s)^5


So multiply them to get the following


1*(3v)^5*(s)^0
5*(3v)^4*(s)^1
10*(3v)^3*(s)^2
10*(3v)^2*(s)^3
5*(3v)^1*(s)^4
1*(3v)^0*(s)^5


1*(243v^5)*(1)
5*(81v^4)*(s)
10*(27v^3)*(s^2)
10*(9v^2)*(s^3)
5*(3v)*(s^4)
1*(1)*(s^5)


243v^5
405sv^4
270s^2v^3
90s^3v^2
15s^4v
s^5


Then add up all the terms to get this final answer


243v^5 + 405sv^4 + 270s^2v^3 + 90s^3v^2 + 15s^4v + s^5


So


(3v+s)^5 = 243v^5 + 405sv^4 + 270s^2v^3 + 90s^3v^2 + 15s^4v + s^5